Neurons and Other Excitable Cells

We study collective failures in biologically realistic networks that consist of coupled excitable units. The networks have broad-scale degree distribution, high modularity, and small-world properties, while the excitable dynamics is determined by the paradigmatic FitzHugh–Nagumo model. We consider different coupling strengths, bifurcation distances, and various aging scenarios as potential culprits of collective failure. We find that for intermediate coupling strengths, the network remains globally active the longest if the high-degree nodes are first targets for inactivation. This agrees well with previously published results, which showed that oscillatory networks can be highly fragile to the targeted inactivation of low-degree nodes, especially under weak coupling. However, we also show that the most efficient strategy to enact collective failure does not only non-monotonically depend on the coupling strength, but it also depends on the distance from the bifurcation point to the oscillatory behavior of individual excitable units. Altogether, we provide a comprehensive account of determinants of collective failure in excitable networks, and we hope this will prove useful for better understanding breakdowns in systems that are subject to such dynamics.

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Determinants of collective failure in excitable networks

Barać

Perc

Gosak

2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Emergence of bursting in a network of memory dependent excitable and spiking leech-heart neurons

Sharma

Mondal

et al. 2020

J. R. Soc. Interface.

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Excitable cells often produce different oscillatory activities that help us to understand the transmitting and processing of signals in the neural system. The diverse excitabilities of an individual neuron can be reproduced by a fractional-order biophysical model that preserves several previous memory effects. However, it is not completely clear to what extent the fractional-order dynamics changes the firing properties of excitable cells. In this article, we investigate the alternation of spiking and bursting phenomena of an uncoupled and coupled fractional leech-heart (L-H) neurons. We show that a complete graph of heterogeneous de-synchronized neurons in the backdrop of diverse memory settings (a mixture of integer and fractional exponents) can eventually lead to bursting with the formation of cluster synchronization over a certain threshold of coupling strength, however, the uncoupled L-H neurons cannot reveal bursting dynamics. Using the stability analysis in fractional domain, we demarcate the parameter space where the quiescent or steady-state emerges in uncoupled L-H neuron. Finally, a reduced-order model is introduced to capture the activities of the large network of fractional-order model neurons.

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Neurons and Other Excitable Cells

Cited by 2 publications

References 129 publications

Determinants of collective failure in excitable networks

Determinants of collective failure in excitable networks

Emergence of bursting in a network of memory dependent excitable and spiking leech-heart neurons

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